Finding distance -- Find the height of an object given ratio of two distances

In summary, the body is dropped from a height of 125m, and the ratio of the distances traveled in (n-3) seconds to the (n-3)rd second is 4:3.
  • #1
D.Man Hazarika
7
0

Homework Statement


A body is dropped from certain height H. If the ratio of the distances traveled by it in (n-3) seconds to (n-3)rd second is 4:3, find H (take g= 10 m/s²) (answer: 125m)

Homework Equations

The Attempt at a Solution


I did this way but I came to a dead end...
To find H,
s= 1/2 gt²
= 1/2 * 10 * (n-3)²
= 5*(n²-9)
= 5n²+45...(I)

S nth = u+g/2(2n-1)
= 5(2n-1)
= 10n-5...(II)
equating (I) AND (2)
5n²+45= 4
________ ___

10n-5. 3

=> 3(5n²+45)=4(10n-5)
=> 15n²+135=40n-20
=> 15n²-40n=-20-135
=> 15n²-40n=-155
=> 15n²+155=40n
=> 15n²+155= 40
____________
n

This is a dead end...what should I do next...?
 
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  • #2
The problem statement looks incomplete. What is n? Is n the number of seconds required to fall the distance H?

Ok, you need to check your algebra a bit. (n-3)^2 is not (n^2 - 9). And 5 (n^2-9) is not 5n^2 + 45. And what are (I) and (II) and why should they be equal?

Also, you need to be using the ratio you have been given. The distance in n-3 seconds is 4/3 the distance in the (n-3)rd second.
 
  • Like
Likes D.Man Hazarika
  • #3
Thanks...rechecking my algebra
 

1. How do you find the height of an object given a ratio of two distances?

To find the height of an object given a ratio of two distances, you will need to use the principle of similar triangles. First, measure the distance from the base of the object to your eye. Then, measure the distance from the top of the object to your eye. Finally, divide the two distances to get the ratio. Next, measure the actual distance from your eye to the object. Multiply this distance by the ratio to get the height of the object.

2. What if I don't have access to the object but only its image or photograph?

If you only have access to the image or photograph of the object, you can still use the same method as described above. However, you will need to know the scale or size of the image. Measure the distance from the base of the image to your eye and the distance from the top of the image to your eye. Divide these distances to get the ratio. Then, measure the actual distance from your eye to the object in the image. Multiply this distance by the ratio to get the height of the object.

3. Can this method be used for both tall and short objects?

Yes, this method can be used for both tall and short objects as long as the distance from your eye to the object is measurable. However, for very tall objects, it may be difficult to accurately measure the distance from the top of the object to your eye. In this case, you can use a measuring instrument such as a laser rangefinder to get a more precise measurement.

4. Is this method accurate for objects that are not perfectly vertical?

This method assumes that the object is perfectly vertical, so it may not be as accurate for objects that are tilted or slanted. To make the measurements more accurate, try to position yourself directly in front of the object and measure the distance from the base of the object to your eye and the distance from the top of the object to your eye.

5. Are there any other methods to find the height of an object given a ratio of two distances?

Yes, there are other methods to find the height of an object given a ratio of two distances. One method is to use trigonometry and the angle of elevation or depression to calculate the height of the object. Another method is to use a measuring instrument such as a clinometer to directly measure the height of the object. However, the method described above is a simple and accurate method that can be used with only a few measurements and basic math calculations.

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